# Lesson: Input/Output Tables: Determining the Rule

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### Lesson Objective

SWBAT determine the rule for an input/output table

### Lesson Plan

Materials Needed: DN Worksheet, Charts for lesson, white board, dry erase markers, and, IND Practice Worksheet.
Vocabulary: input/output table, operations, rule, expression, and equation.

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Do Now (2 - 3 min): The teacher passes out the DN worksheet with one question about total cost to review a previous lesson.

Opening (2 -3 min): Teacher opens by reviewing the answers to the DN. The teacher then states the objective, “Yesterday we learned test taking strategies to help us with identify the total price given the unit cost. Today, we are going learn about input/output tables. By the end of the lesson, you will be able to determine the rule for an input/output table.”

Direct Instruction/Guided Practice (15 - 20 min): Teacher explains, “Raise a silent hand if you have seen an input/output table before? Input/output tables are tables with two columns of numbers, the first is the input, or the number we start with, the second column is the output, the number that we end up with. Now, input numbers are changed in some way to produce the output number. Close your eyes and image an number going into  box on a conveyor belt and then coming out of the box a completely different number. That is what an input/output table does. All input/output table all have a RULE, which means one rule changes all the input numbers into output numbers. Today, we are going to learn how to determine the RULE. The rule is the equation you use to get the output number. For example a rule could look like x + 7, x -3, or x * 6. I used x to represent the input number. Ok, now lets look at the first step to finding the rule. To determine the rule for any input/output table you first need to look at the relationship between the input number and the output number. If the number increases you know the rule includes either addition or subtraction. If the decreases you know the rule includes subtraction or addition. Watch as I determine the rule for this input output table (Chart 2).”  The teacher walks through solving the input/output table in the following matter:

Step 1: Relationship between input/output number
Step 2: Operation Options
Step 3: Try our options on 2 numbers
Intended Answer: Let me try addition, to go from 5 to 20, what would I have to add. Right, 15! I would have to add 15. Ok, now I have to check the second number, because my rule has to work with every number. 6+15 = 21, NOT 24. Ok, darn, that can’t be my rule because it didn’t work for my second number. So, now I know I have to try multiplication. I have to figure out what I multiple 5 by to get to 20. Oh, right 4! Let me try it out with my second number. 6 x 4 = 24. Oh that works.
Step 4: Check our Rule with each number.
Intended Answer: 7x4 =28; 8x4 = 32; 9x4=36; 10x4 =40
Step 5: Write the rule

The teacher continues, “Ok, now that you have watched me find the rule to a input/output table can anyone tell me what the rule I found was? [intended answer: x * 4, students are likely to answer *4]” The teacher then works through another input/output table (Chart 3) with the students calling on the students to answer each step.

Step 1: Relationship between input/output number
Step 2: Operation Options
Step 3: Try our options on 2 numbers
Intended Answer: Let me try subtraction 10-7=3; 11-7=4
Step 4: Check our Rule with each number.
Intended Answer: 12 -7= 5; 13-7= 6; 14-7= 7; 15-7=8 .
Step 5: Write the rule